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What are some mathematical basic number properties?

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Quick Answer

The three major basic properties of numbers in mathematics are the commutative, associative and distributive properties. Other important number properties include the properties of zero and the identity property of multiplication.

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The commutative property applies to addition and multiplication of numbers and basically states that the order of addition or multiplication does not affect the answer. For example, 15 + 14 = 29, and 14 + 15 = 29. Likewise, 10 x 12 = 120, and 12 x 10 = 120. The same principle holds true no matter how many numbers are added or multiplied together.

The associative property also applies to addition and multiplication. This property states that it does not matter which numbers are grouped together in an addition or multiplication problem containing three or more addends or factors. For example, (10 + 11) + 12 = 33, and 10 + (11 + 12) = 33. Similarly, (2 x 3) x 4 = 24, and 2 x (3 x 4) = 24.

The distributive property of numbers helps explain problems dealing with both addition and multiplication. For example, a relevant mathematical problem may ask, "If Bob makes $100 a day and Don makes $200 dollars a day, how much do they both make in two days?" The problem can be set up as follows: 2($100) + 2($200) = 2($100 + $200). Together they make $600.

The properties of zero state that zero added to any number equals that number, and any number multiplied by zero equals zero. Any number added to its negative also equals zero. The identity property of multiplication states that multiplying any number by one does not change the number.

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